Finite Group Databasebeta

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C2×C4×C52×C7×C8 #72189686

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5898240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5

Aliases

abelianC2×C4×C52×C7×C8
multiplicative(ℤ/13079)ˣ, (ℤ/14555)ˣ, (ℤ/15455)ˣ, (ℤ/21075)ˣ, (ℤ/26158)ˣ, (ℤ/28100)ˣ, (ℤ/29110)ˣ, (ℤ/30910)ˣ, (ℤ/42150)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C52×C7
socle, prime radicalC23×C52×C7C2×C4
LCSG ▷ C1
UCSC1 ◁ G

1296 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C52×C7×C16, C2×C52×C7×C82, C42×C52×C7×C8, …
maximal normal subgroup ofC2×C4×C52×C7×C16, C2×C52×C7×C82, C42×C52×C7×C8, …
maximal quotient ofC2×C4×C52×C7×C16, C2×C52×C7×C82, C42×C52×C7×C8, …
automorphism group ofC11×C29×C41
outer automorphism group ofC11×C29×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.